An attempt is made to formulate a specified type of “bulk sampling” as an abstract field for general study. Recommendations are made for definitions of terms. Populations involved are described and means are defined. The problems of randomness, bias and blending are discussed. The formulation of theoretical variance models and their use in attaining optimum sampling plans are illustrated with particular reference to fertilizer and coal. The need for large amounts of empirical research and the desirability of current controls are indicated.